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Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theoryby Paul-Hermann Balduf.
Author:	Balduf, Paul-Hermann.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xvi, 363 p. :ill. (some col.), digital ;24 cm.
Notes:	"Doctoral thesis accepted by Humboldt University of Berlin, Germany."
Contained By:	Springer Nature eBook
Subject:	Renormalization (Physics)
Online resource:	https://doi.org/10.1007/978-3-031-54446-0
ISBN:	9783031544460$q(electronic bk.)

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory
Balduf, Paul-Hermann.

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory[electronic resource] /by Paul-Hermann Balduf. - Cham :Springer Nature Switzerland :2024. - xvi, 363 p. :ill. (some col.), digital ;24 cm. - Springer theses,2190-5061. - Springer theses..

"Doctoral thesis accepted by Humboldt University of Berlin, Germany."

Introduction to perturbative quantum field theory -- Hopf algebra theory of renormalization -- Renormalized Green functions in kinematic renormalization -- Renormalization group and Dyson-Schwinger equations in non-kinematic renormalization -- Field diffeomorphisms and symmetries -- Conclusion and outlook.

This book offers a systematic introduction to the Hopf algebra theory of renormalization in quantum field theory. Special emphasis is put on physical motivation for mathematical constructions, the role of Dyson-Schwinger equations (DSEs), renormalization conditions, and the renormalization group. The bulk of the book deals with the similarities and differences between two popular renormalization conditions, kinematic renormalization (MOM) and Minimal Subtraction (MS) MOM is a physical global boundary condition for Green functions. DSEs can then be solved in terms of power series which only involve finite renormalized quantities. Conversely, MS is defined order-by-order based on divergences of the unrenormalized Green function. We show that MS is equivalent to MOM with coupling-dependent renormalization point. We determine the large-order growth of series coefficients in different renormalization schemes and derive a novel analytic formula for the all-order solution of linear DSEs in MS. Finally, we derive the changes in off-shell Green functions and counterterms under nonlinear redefinition of field variables for self-interacting scalar fields. The book is aimed at mathematically oriented physicists and physically interested mathematicians who seek a systematic overview of the Hopf algebra theory of renormalization and DSEs.

ISBN: 9783031544460$q(electronic bk.)

Standard No.: 10.1007/978-3-031-54446-0doiSubjects--Topical Terms:

306533
Renormalization (Physics)

LC Class. No.: QC174.17.R46

Dewey Class. No.: 530.143

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory
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520 $a This book offers a systematic introduction to the Hopf algebra theory of renormalization in quantum field theory. Special emphasis is put on physical motivation for mathematical constructions, the role of Dyson-Schwinger equations (DSEs), renormalization conditions, and the renormalization group. The bulk of the book deals with the similarities and differences between two popular renormalization conditions, kinematic renormalization (MOM) and Minimal Subtraction (MS) MOM is a physical global boundary condition for Green functions. DSEs can then be solved in terms of power series which only involve finite renormalized quantities. Conversely, MS is defined order-by-order based on divergences of the unrenormalized Green function. We show that MS is equivalent to MOM with coupling-dependent renormalization point. We determine the large-order growth of series coefficients in different renormalization schemes and derive a novel analytic formula for the all-order solution of linear DSEs in MS. Finally, we derive the changes in off-shell Green functions and counterterms under nonlinear redefinition of field variables for self-interacting scalar fields. The book is aimed at mathematically oriented physicists and physically interested mathematicians who seek a systematic overview of the Hopf algebra theory of renormalization and DSEs.
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